Heat oven to 350.
Clean any dirt off of the mushrooms using a damp paper towel and remove the stems. Set mushroom caps aside.
Melt butter in a small skillet. Add breadcrumbs. Cook until breadcrumbs are toasted and turn brown. Remove from heat. Set aside.
Finely dice the stems of the mushroom. Measure out 1 cup of diced mushroom stems. Discard the rest.
Heat olive oil in a large nonstick skillet over medium heat. Add chopped mushroom stems, onion, and garlic.
Cook for 3-4 minutes.
Stir in parsley, thyme, and salt. Cook for 2-3 more minutes until the veggies are soft.
Remove from heat.
Stir in toasted bread crumbs and Parmesan cheese.
Place mushroom caps in an 8x8 inch baking dish, cap side (top) down.
Pour wine into the bottom of the dish.
Spoon 1-2 tsp of the stuffing mixture into each cap, heaping them as full of filling as you’d like.
Cover the dish with aluminum foil and place in your preheated oven.
Bake covered for 20 minutes.
Remove the foil. Sprinkle the stuffed mushrooms with shredded mozzarella cheese, dividing the cheese evenly between the mushrooms.
Bake uncovered for an additional 10 minutes.
Serve your stuffed mushrooms warm. (Not at room temperature.)
Store the leftover mushrooms in an airtight container in the refrigerator for up to 4 days.